A model of the electrical sheath between plasma and a positively biased wall has been developed for the case of the magnetic field perfectly parallel to the wall. The magnetized sheath and relatively large positive wall potential with respect to the plasma are considered, so that only electron current is present in the sheath. We show that the sheath thickness increases linearly with duct current density. There is good quantitative agreement between the calculated and experimental current–voltage duct characteristics. © 1998 American Institute of Physics.